21. a) Evaluate the following limits. Show proper steps. 8x²-2x-3 2x+1 a) lim x→→ 2 2x x-0 √2x+1-1 b) lim

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Q: Evaluate the following definite integral. Provide your answer below: Lax√812²-81 dx

A: The given integral is 8/[x sqrt(81x2-81)], limit from sqrt(2) to 2.

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Q: Find the first partial derivatives of the function. Əw au Əw əv || || W ev u+v8 -e¹ (u+v²)² X

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A: 19) Where, S is the upward-facing paraboloid  lying in cylinder From above curves the radius of the…

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Q: ²1+²² dt 17. y=0 tane de Ꮎ dᎾ 15. y= 16. y -cos²0 de 18. y =√1 + 1² dt - L.

A: We have to Determine the derivative of the function.

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A: Given :- To Evaluate :- The given integral.

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Q: q13.2 You have been given the following equation of a sphere (x^2) + (y^2) + (z^2) - 6x + 4z = 3…

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A: A sphere is given having a hole and we need to find out the volume of the resulted solid.

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A: The radius of each helix is about 10 angstroms(1 Å = 10–8 cm)Each helix rises about 34 Å during each…

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Q: Evaluate the integral. (Use C for the constant of integration.) [s sin5(t) cos6(t) dt

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Q: Compute the following two indefinite integrals showing ALL steps. Remember to include the constant…

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Q: 2. Use the definition of the derivative to find the derivative of, V(t)=3-14t 3. Use the definition…

A: Sol:-  Def:The derivative of a function is the rate at which the function is changing at any given…

Q: Thank you so much. The answer is correct. Could you please answer the second question?

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Q: [.. I (x2+4)2 da First we will do the indefinite integral I S da (x²+4)2 (a) Use the substitution =…

A: We solve this integration problem by using general property of integral.

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Q: Suppose f(x) and f'(x) have the values shown. X 0 1 2 3 f(x) 10 8 9 7 f'(x) 7 8 6 4 5 4 3 لا Let y³…

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Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

A: Convert partial fraction decomposition of the function

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A: As per bartleby guidelines only one question is allowed to solve with maximum 3 sub parts , so here…

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Q: Integral 2 25x²-81 S X -dx

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Q: 7. Given vectors ū= -2ï- 3j+ k, v= 3i+j-2kand w=(3,0,5), find if possible: a) |ū-3v +2w | b) The…

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Q: Let f(x)=(1) and g(x) = 2x. For all x-values, g(x) > f(x). O True 4 False

A: At x=0 then f(x)=(1/2)^0=1 and g(x)=2^0=1

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A: We have,  f(x) = √(x+4) /ln(9-x)

Q: ←++ -10-9-8-7 (If the limit does not exist, enter Ø.) 10 9 8 7 6 5- 4+ 3+ 2+ 1+ -3+ Y -4- II T ст н…

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A: For the function shown  in the graph, to give the interval(s) where the  rate of change of  with…

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